So what happens when make a film with an ultra-confusing narrative arc and with alternating timelines?
You color code that bad boy. You make some of the scenes in color and some in black and white. This decision may seem like a small one but it helps the audience follow the story, making sure they feel a correct amount of confusion and aren't completely overwhelmed.
The black and white scenes happen chronologically prior to the color scenes, which was a natural choice because black and white makes us think "old." These scenes take an overall very short time (both in real time and movie time), provide plenty of exposition, and happen chronologically. They're basically the grounding point.
This color-coding also serves us well in the penultimate scene, where we see the film change from black and white to color, letting us know that our two converging timelines have finally collided. Thanks, Christopher Nolan.